Problem 4 · 2024 Math Kangaroo
Easy
Logic & Word Problems
careful-counting
Mona wants to draw the figure shown without lifting her pen. The lengths of the segments are given. Mona can start anywhere and may go over segments more than once. What is the minimum distance, in centimetres, that Mona has to move her pen across the paper?
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Answer: B — 7 cm
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Hint 1 of 2
If you could draw the whole figure in one stroke without repeating, the pen distance would just be the total length of all the segments.
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Hint 2 of 2
Because some corners have an odd number of segments meeting, you must go over one short segment a second time; add that retraced length to the total.
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Approach: total segment length plus the unavoidable retraced piece
- Add the lengths of all the segments in the figure: 3 + 2 + 1 = 6 cm if nothing is repeated.
- A non-stop drawing can avoid repeats only when at most two corners have an odd number of segments; here too many corners are odd, so one segment must be traced twice.
- The cheapest segment to repeat is the 1 cm piece, adding 1 cm: 6 + 1 = 7 cm.
- The minimum pen distance is 7 cm.
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